The present invention is generally related to a signal processing system for either a magnetic disk apparatus or an optical disk apparatus. More specifically, the present invention is directed to a high-efficiency demodulating method of a high-order partial response system such as an EEPRML (Extended Extended Partial Response Maximum Likelihood) signal processing system and an EEEPRML (Extended EEPRML) signal processing system.
In magnetic disk apparatuses, the partial response maximum likelihood (will be abbreviated as a “PRML” hereinafter) signal processing system combining the partial response class 4 (PR4) and the maximum-likelihood decoding system are practically available as a high-efficiency signal processing system. A high-efficiency signal processing system implies a system capable of realizing a desirable data error rate at a low SIN (signal-to-noise) ratio. Very recently, such high order partial response systems have been practically utilized as signal processing systems capable of reproducing signals at SIN ratios lower than that of the PRML system, for instance, the EPRML system by combining the EPR4 (Extended PR4) with the maximum (most) likelihood decoding system.
FIG. 1 shows a structural example of the construction of a general magnetic disk apparatus using a PRML signal processing system. Original data is supplied to an error correcting encoder 7 through an interface circuit 8 so that the original data is added with redundant data necessary for error correction. Next, the original data added with redundant data is subjected by a data modulator 6 to modulation necessary for the PRML system and is recorded on a magnetic disk 3 by a magnetic head 4 through a recording/reproducing amplifier 5. A signal reproduced from the magnetic disk 3 is passed through the recording/reproducing amplifier 5 and then PRML-processed by a data demodulator 1. The demodulated data is error-corrected by an error correcting decoder 2 and is thereafter converted through the interface circuit 8 into the original data. The operation and the arrangement of this data modulator 6 and data demodulator 1 will now be explained in more detail with reference to FIG. 2 indicating a relationship between a magnetic recording/reproducing system and a partial response system. A first description will now be made of process operations executed on the data recording side. The data outputted from the error correcting encoder 7 is penetrated through a precoder 9 constructed of a delay element and modulo (Mod. 2), and then is recorded via a recording amplifier 5 on a recording medium. This precoder 9 is employed so as to prevent erroneous propagation of data which is caused during the demodulating operation.
Next, a description will now be made of a processing operation on the reproducing side. The magnetization on the recording medium is reproduced as a waveform having a differential characteristic by the recording/reproducing head. PR4 may regard this differential characteristic as a differential system of (1−D). In this case, symbol AD@ implies a 1-bit delay calculator. The reproduced waveform is supplied to the equalizer 10 so as to be equalized in such a manner that a response of the waveform becomes (1+D). As a result, a total transfer characteristic in the output of the equalizer becomes (1−D2). Thereafter, a data discrimination of the data is carried out in the maximum decoder 11. FIG. 3 represents a response of a regenerative isolated waveform (note that a step response will be simply referred to as an “isolated waveform” hereinafter) in the case that a step waveform is magnetically recorded. PR4 implies that the isolated waveform is regarded as a waveform enlarged to 2 time slots, as indicated in FIG. 3A. This waveform owns such a characteristic having (1+D). Also, as indicated in FIG. 3B, EPR4 implies that the isolated waveform is regarded as a waveform enlarged to 3 time slots. This waveform owns such a characteristic having (1+D)2. Furthermore, as indicated in FIG. 3C, EEPR4 implies that the isolated waveform is regarded as a waveform enlarged to 4 time slots. This waveform owns such a characteristic having (1+D)3.
While considering the EEPR4 system as an example, the high order partial response system will now be summarized.
A total transfer characteristic of EEPR4 constitutes (1−D)×(l+D)3 as a product of a transfer characteristic of an isolated waveform and another transfer characteristic of a magnetic recording system. An impulse response of the EEPR4 system determined by this product is represented in FIG. 4. As apparent from a waveform “a” shown in FIG. 4, an isolated waveform of EEPR4 owns amplitude characteristics (normalized ratio) of 1, 3, 3, 1 every bit period. As a consequence, as indicated in a waveform “b” of FIG. 4, a response of an isolated pulse is obtained by superimposing the isolated waveforms inverted along the upper/lower directions with each other by shifting a 1-bit time period. In other words, the response of the isolated pulse becomes 1, 2, 0, −2, −1. In FIG. 5, there is shown a trellis diagram of EEPRML obtained by combining a maximum likelihood decoder with EEPR4. As is well known in this field, the operation of the EEPRML system may be explained based upon the trellis diagram. In the drawing, symbol “ak” indicates an input signal to EEPRML at a time instant “k”. In this case, reference numeral 12 indicates a state, and reference numeral 13 shows a state transition. An upper stage of a label (ak/yk) and a lower stage thereof indicate an input signal value and an output signal value, respectively. The states of the respective signal processing systems are determined by the past input signal series. In EEPRML, a level of a reproduction signal at the present time instant is influenced by signals over the past 4 time slots. Assuming now that a state at a time instant “k” is equal to “sk”, it is given as
sk=((ak−4, ak−3, ak−2, ak−1)1ak(1,0)), and a total number of states becomes 16. At a time instant “k−1”, state transitions originated from a plurality of states are collected to a specific state at the time instant “k”. With respect to these state transitions, a squared value of a difference between an output signal and an input signal, which are indicated at a low stage of each label, will be referred to as a “branch metric”. Also, an accumulated value of branch metrics until the present time instant with respect to each of the states will be referred to as a “path metric”. Among the state transitions collected to a specific-state at the time instant “k”, only such state transitions that a summation becomes a minimum value and this summation is made from path metrics until a time instant “k−1” and branch metrics corresponding to the respective state transitions are selected as a state transition (path) capable of satisfying a maximum likelihood condition (most certain). This stage may be subdivided into the below-mentioned steps. In other words, the path metrics are added to the branch metrics (Add). Next, these added values are compared with each other every state, and such a state transition which becomes a minimum value is selected (Select). A series of these operations will be abbreviated as an “ACS”. The maximum (most) likelihood decoding method is such well-known method that this ACS operation is repeatedly performed at each time instant and under each state, and then when the path metrics are finally converged onto one path on the trellis diagram, the data is determined.
The performance of EEPRML is determined by a minimum free distance (Dfree). In this case, “Dfree” implies a minimum difference of path metrics among various sorts of combinations from a specific node to another specific node on the trellis diagram shown in FIG. 5. It is known that “Dfree” of EEPRML is equal to 6. Furthermore, distances between signals subsequent to “Dfree” become 8 and 10. These distances between signals of EEPRML are determined by a data pattern entered into the maximum likelihood decoder. In particular, a distance between-signals is defined by a continuous time at which a pattern is changed from 0 to 1, or from 1 to 0. As will be discussed later, assuming now that an inverting position contained in a pattern is expressed by, for example, “p”, in such a case that 2 sorts of patterns are set under 1-bit shifted condition, and these patterns own 3-time continuous inverting positions such as “p+p”, a distance between these patterns may give “Dfree”. To further improve the performance of these EPRML system and EEPRML system, very recently, Maximum Transition Run Code (will be abbreviated as an “MTR code” hereinafter) has been proposed.
For instance, the conventional MTR code is described in, for example, “Maximum Transition Run Codes for Data Storage Systems”, IEEE Transactions on Magnetics, volume 32, No. 5, September 1996, pages 3992 to 3994. The above-described MTR code owns a function to restrict that inverting of a pattern occurs more than 3 times. When this MTR code is used, a limitation can be made to the pattern inversion for more than 10 distances between signals of EEPRML. As a consequence, an S/N ratio of a signal can be equivalently improved. However, in the MTR code, the code rate becomes 4/5 and the like. This code rate value is low, as compared with the normally used 16/17 GCR (Group Coded Recording) and 8/9 GCR. As a result, a code rate loss becomes large, and a total coding gain cannot be always satisfied. Concretely speaking, a gain becomes approximately 2.2 dB, since the distance between signals is improved-from 6 to 10. On the other hand, a code rate loss becomes larger than approximately 1 dB under normalized line density=3, for instance, (normalized line density=a half bandwidth of a reproduced waveform is normalized by a width of a recording pulse), and a total coding gain becomes at maximum approximately 1 dB, depending upon a recording density of a magnetic disk.